Problem: Determine the intercepts of the line. $y+5=2(x+1)$ $y$ -intercept: $\Big($
The $y$ -intercept of a graph is the point of intersection between the $y$ -axis and the graph. Since the $y$ -axis is also the line $x=0$, the $x$ -value of this point will always be $0$. The $x$ -intercept of a graph is the point of intersection between the $x$ -axis and the graph. Since the $x$ -axis is also the line $y=0$, the $y$ -value of this point will always be $0$. To find the $y$ -intercept, let's substitute $ x= 0$ into the equation and solve for $y$ : $\begin{aligned}y+5&=2({0}+1)\\ y+5&=2\\ y&=-3\end{aligned}$ So the $y$ -intercept is $\left(0,-3\right)$. To find the $x$ -intercept, let's substitute $ y= 0$ into the equation and solve for $x$ : $\begin{aligned}{0}+5&=2(x+1)\\ 5&=2x+2\\ 3&=2x\\ 1.5&=x\end{aligned}$ So the $x$ -intercept is $\left(1.5,0\right)$. In conclusion, The $y$ -intercept is $\left(0,-3\right)$. The $x$ -intercept is $\left(1.5,0\right)$.